composeN.hs

{-# LANGUAGE DataKinds #-}
{-# LANGUAGE GADTs #-}
{-# LANGUAGE PolyKinds #-}
{-# LANGUAGE TypeOperators #-}
{-# LANGUAGE TypeFamilies #-}
module ComposeN where

type family FunctionType (as :: [k]) (r :: k) :: k where
  FunctionType '[] r = r
  FunctionType (a ': as) r = a -> FunctionType as r

data Nat (as :: [k]) where
  Z :: Nat '[a]
  S :: Nat as -> Nat (a ': as)

composeN :: Nat as -> (b -> c) -> FunctionType as b -> FunctionType as c
composeN Z f g = f . g
composeN (S as) f g = \x -> composeN as f (g x)

add3 :: Int -> Int -> Int -> Int
add3 a b c = a + b + c

test1 :: Int
test1 = composeN (S Z) (+1) (+) 2 3

test2 :: Int
test2 = composeN (S (S Z)) (+1) add3 1 2 3